Assessing network vulnerability using shortest path network problems

Partial Node Failure in Shortest Path Network Problems

“…The first possible direction is to implement the arc flow constraint or node flow constraint in the numerical experiment if information on the arc capacity or node capacity is available. As underscored by a study by Ye and Kim [11] and a nuance from the results in Figure 4, the impact of nodal disruption can manifest differently geographically over the network when arc capacity for flow distributions is considered than when considering the results from non-capacitated models. A second possible direction involves analyzing the reassignment of unrealized flows (i.e., flows departing from and arriving at the partially failed node) at the partially failed node-a possibility that nonetheless has not been considered in this paper, for two reasons: First, the amount of unrealized flows could be easily identified by looking at ridership at status quo; second, reassignment of these flows at the partially failed node could be complicated by other modes in practice (e.g., it is uncertain how passengers or cargos would access the network by connecting to other transportation modes such as bus, taxi, bicycle, or even foot).…”

“…Note that the unrealized trips departing from or arriving at MT C are not taken into account when Ω Pc is computed, because the trip from node C cannot be delivered. Thus, for fair comparison, the network cost related with MT C at status quo (which is 10 passenger*miles) is deducted from the total network cost at status quo (Ω sq−c = 34 − 10 = 24), resulting in a reroute cost when MT C partially fails of 4 passenger*miles calculated by Equation (11). For ViaFlow, when MT C partially fails, all nodes experience flow decreases except node A, because passengers must reroute through node A, and node A would expect 4 more passengers to pass through than usual (at status quo, no passenger has to pass through node A to reach his or her destination).…”

“…The concept of partial failure has been addressed and applied to multiline networks, such as subway systems and light and heavy rail networks, which are characterized by a unique structure of sub-networks at transfer stations [1,4,11]. Seen from the perspective of traditional accessibility measures, the failure of a network component assumes total loss of function, that is not likely to occur in most network systems.…”

“…The problem of finding the shortest path for a single pair comprising origin and destination has been recognized as a fundamental network problem that has been widely adopted and used in various research and applications, where shortest path is that incurring the least cost as measured by travel distance, time, or ticket price. The mathematical formulation of the classical shortest path problems has been extended based on the applications that include a variety of objective functions and constraints to reflect the specific context to be applied (for recent research, readers may refer to works by [11,[15][16][17][18][19][20][21]). The types of shortest path problems are the (1) single-source shortest path problem, (2) all-pairs shortest path problem, and (3) multi-shortest path problem [22][23][24][25][26][27][28][29][30][31].…”

“…Quite a few methods for assessing the failure of network components (i.e., nodes or links) have been highlighted as a way of measuring the network reliability of transportation systems-information that is directly helpful for network planners and policymakers seeking the best feasible plan [2,5]. Compared with algorithm-based approaches, however, mathematical programming approaches are more flexible in structuring constraints and providing effective modeling, particularly for cases such as all-pairs shortest path problems with facility disruption scenarios, because the specific conditions are easily incorporated into the objective function or translated as constraints [11,25]. In view of this benefit, this research has adopted the mathematical programming approach in the model construction of the SPN Sq and SPN Pr .…”